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3 years ago

If y varies directly as x , and y = 6 when x = 15, find y when x = 25

Mathematics

2 answers:

Dima020 [189]3 years ago

7 0

Step-by-step explanation:

let y=kx, k is constant

when y=6, x=15

6=k x 15

k=0.4

when x=25,

y= 0.4 x 25

y=10

Kisachek [45]3 years ago

7 0

Answer:

y = 10

Step-by-step explanation:

Given that y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 6 when x = 15, thus

6 = 15k ( divide both sides by 15 )

k = $\frac{6}{15}$ = $\frac{2}{5}$

y = $\frac{2}{5}$ x ← equation of variation

When x = 25, then

y = $\frac{2}{5}$ × 25 = 10

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a) We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to $2\pi$ :

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We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to $2\pi$ :

$17 \pi/4 - 2\pi = \frac{9\pi}{4} -2\pi = \pi/4$

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So then $sin(\frac{17 \pi}{4}) = \frac{\sqrt{2}}{2}$

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We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to $2\pi$ :

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For this case we know that $cos (\pi/6) = \frac{\sqrt{3}}{2}$

And we know that $\frac{7\pi}{6}$ is on the III quadrant since is equivalent to 210 degrees. And on the III quadrant the cosine is negative. So then $cos(\frac{19 \pi}{6}) = -\frac{\sqrt{3}}{2}$

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